Average Error: 0.4 → 0.4
Time: 4.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)
double f(double x, double y) {
        double r403363 = 3.0;
        double r403364 = x;
        double r403365 = sqrt(r403364);
        double r403366 = r403363 * r403365;
        double r403367 = y;
        double r403368 = 1.0;
        double r403369 = 9.0;
        double r403370 = r403364 * r403369;
        double r403371 = r403368 / r403370;
        double r403372 = r403367 + r403371;
        double r403373 = r403372 - r403368;
        double r403374 = r403366 * r403373;
        return r403374;
}
↓
double f(double x, double y) {
        double r403375 = 3.0;
        double r403376 = x;
        double r403377 = sqrt(r403376);
        double r403378 = y;
        double r403379 = 1.0;
        double r403380 = r403379 / r403376;
        double r403381 = 9.0;
        double r403382 = r403380 / r403381;
        double r403383 = r403378 + r403382;
        double r403384 = r403383 - r403379;
        double r403385 = r403377 * r403384;
        double r403386 = r403375 * r403385;
        return r403386;
}

Error

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Bits error versus y

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\]
  4. Using strategy rm

  5. Applied associate-/r*0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \color{blue}{\frac{\frac{1}{x}}{9}}\right) - 1\right)\right)\]

  6. Final simplification0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))